EXTENSION OF ESTERMANN'S THEOREM TO EULER PRODUCTS ASSOCIATED TO A MULTIVARIATE POLYNOMIAL

作者：Delabarre Ludovic^*

来源：Bulletin de la Societe Mathematique de France, 2013, 141(2): 225-265.

• multivariables Euler products
• meromorphic continuation
• natural boundary
• cyclotomic polynomial
• rational point on a toric variety

Given a multivariate polynomial h (X-1, ..., X-n) with integral coefficients verifying an hypothesis of analytic regularity (and satisfying h(0) = 1), we determine the maximal domain of meromorphy of the Euler product Pi(p prime) h (p(-s1), ..., p(-sn)) and the natural boundary is precisely described when it exists. In this way we extend a well known result for one variable polynomials due to Estermann from 1928. As an application, we calculate the natural boundary of the multivariate Euler products associated to a family of toric varieties.

• 出版日期2013